My understanding is that part of the problem wasn't just that they wanted to hold her, but that airline regulations mandate that each passenger at least has a seatbelt and oxygen mask. Since Ivy's seat was in a totally different part of the plane, she may not have had an oxygen mask.
I think a lot of the trouble could have been solved by talking to the airline ahead of time and giving them a heads up, and maybe having a doctor's note ready. It's risky to just assume that there won't be an issue, and it's understandable that flight attendants might not know exactly what should be done in this situation. Talking to the airline ahead of time, and following up, might have helped streamline things.
Also, I'm curious what they do when Ivy rides in a car, which I assume she probably does. I don't think there's anything wrong with her parents holding her on the plane since she's small enough, but I'm still curious.
I've traveled with family and friends who have special needs kids. They always call ahead and the airline bends over backwards to accommodate. These people were either too stupid to execute basic common sense, or, they were thinking that someone else on the airplane was going to magically make instant accommodations. Or, they were trying to scam the system somehow. Why, I cannot tell. Why do kids need first class tickets to begin With? Unless they are used to this lifestyle? In which case, what does it say about the parents who felt their special needs kid wasn't worth a first class ticket?